 
Summary: Maximizing Profit in Overloaded Networks
Matthew Andrews
Bell Laboratories, Lucent Technologies
Murray Hill, NJ 07974.
Email: andrews@research.belllabs.com
Abstract We consider the problem of scheduling data in
overloaded networks. We wish to maximize the total profit of
data that is served.
We first consider a single server that has to schedule data over
timevarying channels. This model is motivated by scheduling in
wireless networks. Our objective is to maximize
P
i log R i (t)
where R i (t) is the total amount of data scheduled to user i
by time t. In contrast to most previous work we assume that
the channel conditions are defined by an adversary rather than
a stationary, stochastic process. We give lower bounds on how
competitive an online algorithm can be and show that the bounds
are nearly matched by a simple randomized algorithm.
We also consider a situation in which packets with associated
